%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM795^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:18:54 AM UTC 2026
% Result : Theorem 0.11s 0.28s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 26 unt; 0 typ; 6 def)
% Number of atoms : 285 ( 68 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 381 ( 57 ~; 49 |; 0 &; 254 @)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 60 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
rat: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x0: rat ).
thf(func_def_1,type,
y0: rat ).
thf(func_def_2,type,
z0: rat ).
thf(func_def_3,type,
u0: rat ).
thf(func_def_4,type,
lessis: rat > rat > $o ).
thf(func_def_6,type,
less: rat > rat > $o ).
thf(func_def_7,type,
pl: rat > rat > rat ).
thf(func_def_8,type,
more: rat > rat > $o ).
thf(func_def_9,type,
moreis: rat > rat > $o ).
thf(f1,axiom,
lessis @ x0 @ y0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).
thf(f2,axiom,
less @ z0 @ u0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k) ).
thf(f3,axiom,
! [X0: rat,X1: rat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz82) ).
thf(f4,axiom,
! [X3: rat,X0: rat,X1: rat,X2: rat] :
( ( moreis @ X0 @ X1 )
=> ( ( more @ X2 @ X3 )
=> ( more @ ( pl @ X0 @ X2 ) @ ( pl @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz99a) ).
thf(f5,axiom,
! [X0: rat,X1: rat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz85) ).
thf(f6,axiom,
! [X1: rat,X0: rat] :
( ( less @ X0 @ X1 )
=> ( more @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz83) ).
thf(f7,conjecture,
less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz99c) ).
thf(f8,negated_conjecture,
~ ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
~ ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
( ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) )
!= $true ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: rat,X1: rat] :
( ( less @ X1 @ X0 )
=> ( more @ X0 @ X1 ) ),
inference(rectify,[],[f6]) ).
thf(f12,plain,
! [X0: rat,X1: rat] :
( ( ( less @ X1 @ X0 )
= $true )
=> ( ( more @ X0 @ X1 )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: rat,X1: rat] :
( ( more @ X0 @ X1 )
=> ( less @ X1 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f14,plain,
! [X0: rat,X1: rat] :
( ( ( more @ X0 @ X1 )
= $true )
=> ( ( less @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: rat,X1: rat] :
( ( lessis @ X0 @ X1 )
=> ( moreis @ X1 @ X0 ) ),
inference(rectify,[],[f5]) ).
thf(f16,plain,
! [X0: rat,X1: rat] :
( ( ( lessis @ X0 @ X1 )
= $true )
=> ( ( moreis @ X1 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
lessis @ x0 @ y0,
inference(rectify,[],[f1]) ).
thf(f18,plain,
( ( lessis @ x0 @ y0 )
= $true ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
less @ z0 @ u0,
inference(rectify,[],[f2]) ).
thf(f20,plain,
( ( less @ z0 @ u0 )
= $true ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
! [X0: rat,X1: rat,X2: rat,X3: rat] :
( ( moreis @ X1 @ X2 )
=> ( ( more @ X3 @ X0 )
=> ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f22,plain,
! [X3: rat,X2: rat,X0: rat,X1: rat] :
( ( $true
= ( moreis @ X1 @ X2 ) )
=> ( ( $true
= ( more @ X3 @ X0 ) )
=> ( $true
= ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
( ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) )
!= $true ),
inference(flattening,[],[f10]) ).
thf(f24,plain,
! [X0: rat,X1: rat] :
( ( ( less @ X1 @ X0 )
= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f25,plain,
! [X0: rat,X1: rat] :
( ( ( more @ X0 @ X1 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f26,plain,
! [X3: rat,X2: rat,X0: rat,X1: rat] :
( ( $true
= ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) )
| ( $true
!= ( more @ X3 @ X0 ) )
| ( $true
!= ( moreis @ X1 @ X2 ) ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f27,plain,
! [X0: rat,X3: rat,X1: rat,X2: rat] :
( ( $true
!= ( more @ X3 @ X0 ) )
| ( $true
!= ( moreis @ X1 @ X2 ) )
| ( $true
= ( more @ ( pl @ X1 @ X3 ) @ ( pl @ X2 @ X0 ) ) ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
! [X1: rat,X0: rat] :
( ( ( lessis @ X0 @ X1 )
!= $true )
| ( ( moreis @ X1 @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f29,plain,
! [X0: rat,X1: rat,X2: rat,X3: rat] :
( ( ( more @ X1 @ X0 )
!= $true )
| ( $true
!= ( moreis @ X2 @ X3 ) )
| ( $true
= ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X3 @ X0 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f30,plain,
! [X0: rat,X1: rat] :
( ( ( lessis @ X1 @ X0 )
!= $true )
| ( ( moreis @ X0 @ X1 )
= $true ) ),
inference(rectify,[],[f28]) ).
thf(f31,plain,
( ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) )
!= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f32,plain,
! [X2: rat,X3: rat,X0: rat,X1: rat] :
( ( $true
= ( more @ ( pl @ X2 @ X1 ) @ ( pl @ X3 @ X0 ) ) )
| ( $true
!= ( moreis @ X2 @ X3 ) )
| ( ( more @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f33,plain,
! [X0: rat,X1: rat] :
( ( ( less @ X1 @ X0 )
= $true )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f34,plain,
( ( less @ z0 @ u0 )
= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f35,plain,
( ( lessis @ x0 @ y0 )
= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f36,plain,
! [X0: rat,X1: rat] :
( ( ( moreis @ X0 @ X1 )
= $true )
| ( ( lessis @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f37,plain,
! [X0: rat,X1: rat] :
( ( ( more @ X0 @ X1 )
= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f40,definition,
( spl0_1
<=> ( ( less @ z0 @ u0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f42,plain,
( ( ( less @ z0 @ u0 )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
spl0_1,
inference(avatar_split_clause,[],[f34,f40]) ).
thf(f45,definition,
( spl0_2
<=> ( ( lessis @ x0 @ y0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f47,plain,
( ( ( lessis @ x0 @ y0 )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,plain,
spl0_2,
inference(avatar_split_clause,[],[f35,f45]) ).
thf(f50,definition,
( spl0_3
<=> ( ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f52,plain,
( ( ( less @ ( pl @ x0 @ z0 ) @ ( pl @ y0 @ u0 ) )
!= $true )
| spl0_3 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
~ spl0_3,
inference(avatar_split_clause,[],[f31,f50]) ).
thf(f54,plain,
( ( ( more @ ( pl @ y0 @ u0 ) @ ( pl @ x0 @ z0 ) )
!= $true )
| ( $true != $true )
| spl0_3 ),
inference(superposition,[],[f52,f33]) ).
thf(f55,plain,
( ( ( more @ ( pl @ y0 @ u0 ) @ ( pl @ x0 @ z0 ) )
!= $true )
| spl0_3 ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f57,definition,
( spl0_4
<=> ( ( more @ ( pl @ y0 @ u0 ) @ ( pl @ x0 @ z0 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f59,plain,
( ( ( more @ ( pl @ y0 @ u0 ) @ ( pl @ x0 @ z0 ) )
!= $true )
| spl0_4 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f60,plain,
( ~ spl0_4
| spl0_3 ),
inference(avatar_split_clause,[],[f55,f50,f57]) ).
thf(f63,plain,
( ( $true != $true )
| ( $true
!= ( moreis @ y0 @ x0 ) )
| ( $true
!= ( more @ u0 @ z0 ) )
| spl0_4 ),
inference(superposition,[],[f59,f32]) ).
thf(f64,plain,
( ( $true
!= ( more @ u0 @ z0 ) )
| ( $true
!= ( moreis @ y0 @ x0 ) )
| spl0_4 ),
inference(trivial_inequality_removal,[],[f63]) ).
thf(f66,definition,
( spl0_5
<=> ( $true
= ( more @ u0 @ z0 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f68,plain,
( ( $true
!= ( more @ u0 @ z0 ) )
| spl0_5 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f70,definition,
( spl0_6
<=> ( $true
= ( moreis @ y0 @ x0 ) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f72,plain,
( ( $true
!= ( moreis @ y0 @ x0 ) )
| spl0_6 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f73,plain,
( ~ spl0_5
| ~ spl0_6
| spl0_4 ),
inference(avatar_split_clause,[],[f64,f57,f70,f66]) ).
thf(f74,plain,
( ( ( less @ z0 @ u0 )
!= $true )
| ( $true != $true )
| spl0_5 ),
inference(superposition,[],[f68,f37]) ).
thf(f75,plain,
( ( ( less @ z0 @ u0 )
!= $true )
| spl0_5 ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f76,plain,
( $false
| ~ spl0_1
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f75,f42]) ).
thf(f77,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f76]) ).
thf(f78,plain,
( ( ( lessis @ x0 @ y0 )
!= $true )
| ( $true != $true )
| spl0_6 ),
inference(superposition,[],[f72,f36]) ).
thf(f79,plain,
( ( ( lessis @ x0 @ y0 )
!= $true )
| spl0_6 ),
inference(trivial_inequality_removal,[],[f78]) ).
thf(f80,plain,
( $false
| ~ spl0_2
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f79,f47]) ).
thf(f81,plain,
( ~ spl0_2
| spl0_6 ),
inference(avatar_contradiction_clause,[],[f80]) ).
cnf(s1,plain,
spl0_1,
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f48]) ).
cnf(s3,plain,
~ spl0_3,
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f60]) ).
cnf(s5,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f77]) ).
cnf(s7,plain,
( ~ spl0_2
| spl0_6 ),
inference(sat_conversion,[],[f81]) ).
cnf(s8,plain,
~ spl0_4,
inference(rat,[],[s4,s3]) ).
cnf(s9,plain,
spl0_6,
inference(rat,[],[s7,s2]) ).
cnf(s10,plain,
~ spl0_5,
inference(rat,[],[s5,s8,s9]) ).
cnf(s11,plain,
~ spl0_1,
inference(rat,[],[s6,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11]) ).
thf(f82,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM795^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n020.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 13:00:02 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.28 % (1010167)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.11/0.28 % (1010184)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2466660762:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.11/0.28 % (1010184) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1010167-1010184"...
% 0.11/0.28 % (1010187)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.11/0.28 % (1010184)...printing done.
% 0.11/0.28 % (1010187)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.11/0.28 % (1010184)Refutation found. Thanks to Tanya!
% 0.11/0.28 % SZS status Theorem for theBenchmark
% 0.11/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.28 % (1010184)------------------------------
% 0.11/0.28 % (1010184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.28 % (1010184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.28 % (1010184)CaDiCaL version: 2.1.3
% 0.11/0.28 % (1010184)Termination reason: Refutation
% 0.11/0.28 % (1010184)Time elapsed: 0.003 s
% 0.11/0.28 % (1010184)Peak memory usage: 13 MB
% 0.11/0.28 % (1010184)Instructions burned: 6 (million)
% 0.11/0.28 % (1010167)Success in time 0.035 s
% 0.11/0.28 % Vampire exiting
%------------------------------------------------------------------------------